1992
	Excerpt from a letter to Professor Zadeh

	LETTER TO ZADEH




The particular calculus of combination that fuzzy set semantics implies has
never suited my aesthetics.  During your recent talk, I realized that it is
just a matter of aesthetics.  I know more about linguistic convention than I
used to:  now I see the problem of actually assigning numerical fuzzy degrees
and ramp functions to assertions as just a question of adopting linguistic
convention.  It is hard to say "snow is white to degree .8", but it is also
hard to say "snow is white is a defeasible reasoning policy" and it is hard to
say "snow is white" although most logicians, being unreflective, would be
loathe to admit it.

I believe that this is why your best examples involve the use of language, or
some kind of user-interface (this may help explain why you are revered among
designers of commercial products, and why you think expert systems
applications still are not fully explored).

Despite our differences over the relative beauty of various linguistic
conventions, I will always affirm your importance to the philosophy of logic.
The Western intellectual tradition has required the attribution of properties
and individuation of objects to be crisp, for better or for worse.  Somebody
had to shake things up.

Two more alternatives for escaping the straightjacket of the Western
intellectual tradition, of crisp language, are emerging (we can perhaps add
these to the existing repertoire of fuzzy, probabilistic, and
best-fit/theory-formation methods).

One comes from law, and AI's interest in law, where the idea of linguistic
convention is apt.  It is the idea of an "open-textured" term.

If I create a policy, a rule of law, and say "those whose primary place of
business is their home office may take the home office deduction," I am
inventing terms, such as "primary place of business." Applying this term in
the world is not easy -- an epistemological issue --, and never crisp --
perhaps a semantical issue.  By design, I expect that certain statutes may
help determine the applicability of this term, and the body of cases may help
in larger measure; but ultimately, determining for a particular case whether
the term applies requires a process -- a hearing (whether actual or purely
Gedanken) -- in which pro's and con's are considered.

It is my right (and I exercise it) as a policy-maker to intend this meaning of
my term, just as it is the right of the fuzzy-interlocuter to insist on a
particular shape of the "is-white" membership function.

Like fuzzy linguistic conventions, open-texture has met the resistance of
cynical, narrow-minded, evil(?) colleagues.  Some, for example, have tried to
reduce the non-demonstrative reasoning on which open-texture depends to
various kinds of multi-valued logics.  While the correct path, I believe, is
to formalize the processes of argumentation -- counterargument, rebuttal,
defeat, etc. -- that are appropriate, a multi-valued logic reduction seeks to
reduce the convention to something that it is not.  Just as is the case for
fuzzy logic's relation to multi-valued logic, MVL can be shown to take us a
certain distance, but a qualitative leap is needed to achieve real open
texture (by the way, the concept seems to have originated in jurisprudence).

The other emerging way out of the dominant Western linguistic tradition is
distributed representation.  I can tell from some of your remarks at
Washington University that you have had many discussions with connectionists
and are not happy about their point of view.  I agree that connectionists tend
toward zeal, and can be difficult to talk to.  But just two weeks ago, during
an AI seminar reading, I exclaimed that this distributed representation could
have been a suitable alternative twenty-five years ago for the movement you
led.

As I understand it, something is an instance of a concept only insofar as its
"primitive, distributed" representation is located near the cluster of other
instances of the concept.  Of course, this makes psychologists happy, who can
access k-dimensional scatter plots and who are influenced by Eleanor Rosch.
Regardless of the other wild claims they may make, this does lend a certain
robustness to their models.  It is particularly intriguing when training a
recurrent network results in this automatic clustering, in the same way that
we might generate an error-correcting code, where useable codes are points
that are as Hamming-far apart as possible.

The main response, I would think, is that clustering has always been a way of
creating concepts.  The networks provide no concept of inference and are
therefore not legitimate alternatives to a fuzzy logic.  However, I would not
deny the connectionists the claim that they have achieved a kind of
fuzziness.